The positive energy theorem for asymptotically anti-de Sitter spacetimes

Abstract

We establish the inequality for Henneaux-Teitelboim's total energy-momentum for asymptotically anti-de Sitter initial data sets which are asymptotic to arbitrary $t$-slice in anti-de Sitter spacetime. In particular, when $t=0$, it generalizes Chruściel-Maerten-Tod's inequality in the center of AdS mass coordinates. We also show that the determinant of energy-momentum endomorphism $\mathbf{Q}$ is the geometric invariant of asymptotically anti-de Sitter spacetimes.

24 pages, revised substantially, the new energy-momentum inequality proved. Appeared in Communications in Contemporary Mathematics

References in corpus (3)

• Positive mass theorems for asymptotically AdS spacetimes with arbitrary cosmological constant
• Positive mass theorems for asymptotically de Sitter spacetimes
• Spacelike hypersurfaces with negative total energy in de Sitter spacetime

Cited by in corpus (2)

• Metrics of Eguchi-Hanson types with the negative constant scalar curvature
• Recent progress on the positive energy theorem